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C13×(C31⋊C3)⋊C4 #18012809

order4836
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C31⋊C3)⋊C4
unambiguous semidirect product(C31⋊C3)⋊(C4×C13)
unambiguous semidirect productDic31⋊(C3×C13)

Splittings

derived, SylowC31 ⋊ C3×C4×C13
HallC13×Dic31 ⋊ C3
HallC13×C31⋊C3 ⋊ C4
HallC13×C31 ⋊ C3×C4
HallDic31 ⋊ C3×C13
HallC31⋊C3 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D31⋊C3
commutator, hypocenterC31C3×C4×C13
FrattiniC2C13×D31⋊C3
Fitting, socleC2×C13×C31C2×C3
prime radicalC2×C13×C31⋊C3C2
cosocleC2×C31C2×C3×C13
LCSG ▷ C31
UCSC1 ◁ C2×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 1612

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19,20,16,17,21)(18,27,28,22,23,35)(24,37,38,30,31,43)(25,36,32,33,29,26)(34,44,41,40,39,42)(45,46,47,48);(14,15,18,24,32,20,19,25,34,41,28,36,27,31,39,38,43,44,37,23,29,35,42,40,33,17,21,26,30,22,16)

Conjugacy classes & character table

286 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13⋊C3×(C31⋊C3)⋊C4, C3×C13×(C31⋊C3)⋊C4, C13×C3⋊((C31⋊C3)⋊C4), …
maximal normal subgroup ofC13⋊C3×(C31⋊C3)⋊C4, C3×C13×(C31⋊C3)⋊C4, C5×C13×(C31⋊C3)⋊C4, …
maximal quotient ofC13×Dic31⋊C9, C3×C13×(C31⋊C3)⋊C4, C13×C3⋊((C31⋊C3)⋊C4), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4836, 13);