Finite Group Databasebeta

C2×Dic1304 #23782093

order10432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic1304

Splittings

SylowC163 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D1304
commutator, cosocleC8×C163C23
FrattiniC8C22×D163
FittingC2×C16×C163C2
socle, prime radicalC22×C163D8
hypercenterC2×C16D163
hypocenterC163C2×Q32
LCSG ▷ C8×C163 ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 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#35212716, #35212718, #35212728, …
maximal normal subgroup of#35212716, #35212718, #35212728, …
maximal quotient ofC2×#23781470, C2×#23781491, C4×Dic1304, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 977);