Finite Group Databasebeta

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#123×C43⋊C8 #25103557

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#123×C43⋊C8

Splittings

SylowC43 ⋊ C8×#123

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC4×#123×C43C2
socleC23×C43C23×C4
prime radicalC22×D4×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC4×#123D43
hypocenterC43C8×#123
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#123

1034 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 176528);