Finite Group Databasebeta

C2×Q8×#14556313 #49149014

order36928
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#14556313
unambiguous semidirect productD577⋊(C4×Q8)

Splittings

FittingC2×Q8×C577 ⋊ C4
SylowC577 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#14556313
commutatorC2×C577C23×C4
FrattiniC2C23×#14556313
FittingC2×Q8×C577C4
socleC22×C577C22×C4
prime radicalC22×D577C23
cosocleC2×D577C24
hypercenterC2×Q8#14556313
hypocenterC577C2×C4×Q8
LCSG ▷ C2×C577 ▷ C577
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9232

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 1614);