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C2×C4×#13063266 #25249856

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4×#13063266

Splittings

FittingC2×C4×D8×C43 ⋊ C2
SylowC43 ⋊ C2×C4×D16

Subgroups

subgroupG/H
centerC22×C4#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
cosocleC2×C8×C43C24
hypercenterC2×C4×D8D43
hypocenterC43C2×C4×D16
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

806 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322827);