Finite Group Databasebeta

C2×#19132673 #25011434

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19132673

Splittings

SylowC43 ⋊ C2×#1374

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C2×C4×C16
FrattiniC22×C8C22×D43
FittingC22×C4×C8×C43C2
socle, prime radicalC24×C43C2×C8
cosocleC22×C8×C43C23
hypercenterC22×C4×C8D43
hypocenterC43C2×#1374
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

726 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, 84405);