Finite Group Databasebeta

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C4×Q8×D157 #23757736

order10048
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q8×D157

Splittings

FittingC4×Q8×C157 ⋊ C2
SylowC157 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D157
commutatorC2×C157C23×C4
FrattiniC22C23×D157
FittingC4×Q8×C157C2
socle, cosocleC22×C157C24
prime radicalC22×D157C23
hypercenterC4×Q8D157
hypocenterC157C2×C4×Q8
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofQ8⋊C8×D157, #34098529, #34098563, …
maximal normal subgroup ofQ8⋊C8×D157, #34098529, #34098563, …
maximal quotient ofC4×C4⋊C4×D157, C4×#19097736, C4×Q8×Dic157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1012);