Finite Group Databasebeta

C2×#19136279 #25249426

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

Aliases

direct productC2×#19136279

Splittings

FittingC2×C43×#356 ⋊ C2
SylowC43 ⋊ C2×#2132

Subgroups

subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C23×C4
FrattiniC2×Q8C23×D43
FittingC2×C43×#356C2
socleC22×C43C2×#99
prime radicalC2×#14583450C2
cosocleC2×Q8×C43C24
hypercenterC2×#356D43
hypocenterC43C2×#2132
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

1306 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322397);