Finite Group Databasebeta

C2×#19136379 #25249626

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19136379

Splittings

SylowC43 ⋊ C2×#2158

Subgroups

subgroupG/H
centerC22×C4D344
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC23×C16×C43C2
socleC23×C43C2×D8
prime radicalC24×C43D8
cosocleC2×C8×C43C24
hypercenterC23×C16D43
hypocenterC43C2×#2158
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

694 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322597);