Finite Group Databasebeta

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C4×D4×C92 #72244142

order2592
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C4×C92 · Schur multiplier (H2) = C23×C9

Aliases

direct productC4×D4×C92

Subgroups

subgroupG/H
centerC2×C4×C92C22
commutatorC2C22×C4×C92
Frattini, socle, cosocleC22×C32C23×C32
prime radicalC2×C32×D4C2×C32
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C92 ◁ G

1081 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1296

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,4,3)(6,8)(9,10,11,12,13,14,15,16,17);(1,3,4,2)(18,19,20,21,22,23,24,25,26);(5,6,7,8)

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC4×D4×C9⋊D9, #72254558
maximal subgroup ofC92×#442, C4×D4×C9⋊D9, #72254558
maximal normal subgroup ofC92×#442, C4×D4×C9⋊D9, #72254558
maximal quotient ofC92×#442

GAP

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

gap> G := Group((1,2,4,3)(6,8)(9,10,11,12,13,14,15,16,17), (1,3,4,2)(18,19,20,21,22,23,24,25,26), (5,6,7,8));