Finite Group Databasebeta

C2×D2608 #23782086

order10432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D2608

Splittings

FittingC2×C16×C163 ⋊ C2
SylowC163 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22D1304
commutator, cosocleC8×C163C23
FrattiniC8C22×D163
FittingC2×C16×C163C2
socleC22×C163D8
hypercenterC2×C16D163
hypocenterC163C2×D16
LCSG ▷ C8×C163 ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2614 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35212713, #35212715, #35212725, …
maximal normal subgroup of#35212713, #35212715, #35212725, …
maximal quotient ofC2×#23781467, C2×#23781491, C4×D2608, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 970);