Finite Group Databasebeta

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C22×C4×Q8×D43 #26003164

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×Q8×D43

Splittings

FittingC22×C4×Q8×C43 ⋊ C2
SylowC43 ⋊ C23×C4×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC22×C4×Q8×C43C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC22×C43C26
hypercenterC22×C4×Q8D43
hypocenterC43C23×C4×Q8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

12446 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076135);