Finite Group Databasebeta

← Prev (#24923731) Next (#24923733) →

C4×Q8×D167 #24923732

order10688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q8×D167

Splittings

FittingC4×Q8×C167 ⋊ C2
SylowC167 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D167
commutatorC2×C167C23×C4
FrattiniC22C23×D167
FittingC4×Q8×C167C2
socle, cosocleC22×C167C24
prime radicalC22×D167C23
hypercenterC4×Q8D167
hypocenterC167C2×C4×Q8
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofQ8⋊C8×D167, #36322531, #36322565, …
maximal normal subgroup ofQ8⋊C8×D167, #36322531, #36322565, …
maximal quotient ofC4×C4⋊C4×D167, C4×#19128797, C4×Q8×Dic167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 1012);