Finite Group Databasebeta

← Prev (#22578467) Next (#22578469) →

C2×Q8×#10587739 #22578468

order8768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#10587739
unambiguous semidirect productD137⋊(C4×Q8)

Splittings

FittingC2×Q8×C137 ⋊ C4
SylowC137 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#10587739
commutatorC2×C137C23×C4
FrattiniC2C23×#10587739
FittingC2×Q8×C137C4
socleC22×C137C22×C4
hypercenterC2×Q8#10587739
hypocenterC137C2×C4×Q8
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#101×#10587739, #103×#10587739, #31796562, …
maximal normal subgroup of#101×#10587739, #103×#10587739, #31796562, …
maximal quotient ofC2×C4⋊C4×#10587739, C4×Q8×#10587739, C2×#22578352, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1614);