Finite Group Databasebeta

C2×#21422280 #28509140

order15104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422280

Splittings

SylowC59 ⋊ C2×#1417

Subgroups

subgroupG/H
centerC2×C4#14273668
commutatorC16×C59C22×C4
FrattiniC2×C16C22×D59
Fitting, prime radicalC2×C59×#508C2
socleC22×C59#357
cosocleC2×C16×C59C23
hypercenterC2×#508D59
hypocenterC59C2×#1417
LCSG ▷ C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90019);