Finite Group Databasebeta

C2×#19136453 #25249871

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136453

Splittings

SylowC43 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC23D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#366C2
socle, prime radicalC23×C43C2×D8
cosocleC2×C8×C43C24
hypercenterC2×#366D43
hypocenterC43C2×C4×Q32
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

678 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322842);