Finite Group Databasebeta

← Prev (#27189058) Next (#27189060) →

C3×C7×Dic31⋊C5 #27189059

order13020
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic31⋊C5
unambiguous semidirect product(C3×Dic31)⋊(C5×C7)
unambiguous semidirect product(C3×C7×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C7
HallC3×C7×ΓL(1,𝔽32) ⋊ C4
HallC3×C7×Dic31 ⋊ C5
HallC7×ΓL(1,𝔽32) ⋊ C3×C4
HallC7×Dic31 ⋊ C3×C5
HallC3×C7×C31 ⋊ C4×C5
HallC3×ΓL(1,𝔽32) ⋊ C4×C7
HallC3×Dic31 ⋊ C5×C7
HallC7×C31 ⋊ C3×C4×C5
HallΓL(1,𝔽32) ⋊ C3×C4×C7
HallDic31 ⋊ C3×C5×C7
HallC3×C31 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D31⋊C5
commutator, hypocenterC31C3×C4×C5×C7
FrattiniC2C3×C7×D31⋊C5
Fitting, socleC2×C3×C7×C31C2×C5
prime radicalC2×C3×C7×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 2604

A minimal faithful permutation representation — 2 generators on 45 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 26);