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C2×C32×#359 #11769191

order1152
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C32×#359

Subgroups

subgroupG/H
centerC2×C32×C4D8
commutatorC8C22×C32×C4
Frattini, cosocleC2×C8C23×C32
socleC22×C32#102
prime radicalC2×C32×#135C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C32×C4 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 576

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C32×#2179
maximal normal subgroup ofC2×C32×#2179

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3202);