Finite Group Databasebeta

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Q8×#14273650 #28605292

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#14273650

Splittings

SylowC59 ⋊ Q8×#103

Subgroups

subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingQ8×C4⋊C4×C59C2
socle, prime radicalC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterQ8×C4⋊C4D59
hypocenterC59Q8×#103
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 186171);