Finite Group Databasebeta

← Prev (#11768474) Next (#11768476) →

C32×#1426 #11768475

order1152
nilpotency class5
isoclinismisoclinic class of #1426
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×#1426

Subgroups

subgroupG/H
center, socleC2×C32#367
commutatorC16C2×C32×C4
Frattini, cosocleC2×C16C22×C32
prime radicalC22×C32SD32
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C2×C32×C8 ◁ C2×C32×C16 ◁ G

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 288

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC3⋊D3×#1426, #72255432
maximal subgroup ofC32×#13658, C3⋊D3×#1426, #72255432
maximal normal subgroup ofC32×#13658, C3⋊D3×#1426, #72255432
maximal quotient ofC32×#7463

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2486);