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C4×Q8×D163 #23782128

order10432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q8×D163

Splittings

FittingC4×Q8×C163 ⋊ C2
SylowC163 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D163
commutatorC2×C163C23×C4
FrattiniC22C23×D163
FittingC4×Q8×C163C2
socle, cosocleC22×C163C24
prime radicalC22×D163C23
hypercenterC4×Q8D163
hypocenterC163C2×C4×Q8
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofQ8⋊C8×D163, #35212929, #35212963, …
maximal normal subgroup ofQ8⋊C8×D163, #35212929, #35212963, …
maximal quotient ofC4×C4⋊C4×D163, C4×#19104700, C4×Q8×Dic163, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 1012);