Finite Group Databasebeta

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C22×C4⋊(C43⋊C16) #25249572

order11008
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊(C43⋊C16)

Splittings

SylowC43 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C23×C16
FrattiniC2×C8C23×D43
FittingC22×C4×C8×C43C2
socle, prime radicalC24×C43C2×C8
cosocleC2×C8×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C22×C4⋊C16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

862 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322543);