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C2×C32×#508 #11770460

order1152
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3

Aliases

direct productC2×C32×#508

Subgroups

subgroupG/H
centerC2×C32×C4D8
commutator, Frattini, cosocleC8C24×C32
socleC22×C32C2×D8
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C32×C4 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 40 points:

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

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, 4471);