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C3×A4⋊#595 #72276082

order2448
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×A4⋊#595

Splittings

Fitting, socleC22×C3×C17 ⋊ Dic3
derivedA4×C17 ⋊ C3×C4
SylowC17 ⋊ C3×SL(2,ℤ/4)

Subgroups

subgroupG/H
center, hypercenterC3A4⋊#595
commutator, hypocenterA4×C17C3×C4
FrattiniC1G
Fitting, socleC22×C3×C17Dic3
prime radicalC3×A4×D17C2
cosocleA4×D17C2×C3
LCSG ▷ A4×C17
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

(1,4,3,2)(5,6,7)(9,10,11,13)(12,15,16,20)(14,19,17,18)(21,23,24,22);(2,3,4)(8,9,12,17,13,18,22,24,20,15,21,23,19,10,14,16,11)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,4,3,2)(5,6,7)(9,10,11,13)(12,15,16,20)(14,19,17,18)(21,23,24,22), (2,3,4)(8,9,12,17,13,18,22,24,20,15,21,23,19,10,14,16,11));