Finite Group Databasebeta

Q8×#64541 #14577216

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#64541

Splittings

FittingC2×C4×Q8×C19 ⋊ C2
SylowC19 ⋊ Q8×#41

Subgroups

subgroupG/H
centerC2×C4C23×D19
commutator, socle, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C4×Q8×C19C2
prime radicalC2×#64541C22
hypercenterC2×C4×Q8D19
hypocenterC19Q8×#41
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18074580, #18074584
maximal normal subgroup of#18074580, #18074584

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 18091);