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C4×C112⋊C3 #13089714

order1452
isoclinismisoclinic class of C112⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productC4×C112⋊C3
unambiguous semidirect product(C4×C112)⋊C3

Splittings

Fitting, HallC4×C112 ⋊ C3
derived, SylowC112 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC4C112⋊C3
commutator, hypocenterC112C3×C4
FrattiniC2C2×C112⋊C3
FittingC4×C112C3
socle, cosocleC2×C112C2×C3
prime radicalC2×C112⋊C3C2
LCSG ▷ C112
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4)(5,6,8)(7,11,19)(9,15,23)(10,17,29)(12,22,14)(13,24,18)(16,28,37)(20,25,33)(21,26,35)(27,36,30)(31,34,32);(5,7,12,23,33,36,37,24,34,29,35)(6,18,9,21,16,22,10,30,11,32,20)(8,15,28,17,19,25,13,26,14,27,31)

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×C112⋊C3, C3×C4×C112⋊C3, Dic13⋊(C112⋊C3), …
maximal normal subgroup ofC3×C4×C112⋊C3, C4×C13×C112⋊C3, C4×C17×C112⋊C3, …
maximal quotient ofC4×C112⋊C9, Dic3×C112⋊C3, C3×C4×C112⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1452, 13);