Finite Group Databasebeta

Q8×#67288 #15686978

order2944
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#67288

Splittings

FittingC2×C4×Q8×C23 ⋊ C2
SylowC23 ⋊ Q8×#41

Subgroups

subgroupG/H
centerC2×C4C23×D23
commutator, socle, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C4×Q8×C23C2
prime radicalC2×#67288C22
hypercenterC2×C4×Q8D23
hypocenterC23Q8×#41
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 18091);