Finite Group Databasebeta

Q8×#14556654 #34026406

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#14556654

Splittings

FittingQ82×C73 ⋊ C4
SylowC73 ⋊ Q8×#103

Subgroups

subgroupG/H
centerC22C22×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingQ82×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC22×D73C22×D4
cosocleC2×C4×D73C24
hypercenterQ82#64408
hypocenterC73Q8×#103
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1109990);