Finite Group Databasebeta

C2×#21422325 #28509793

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#21422325

Splittings

SylowC59 ⋊ C2×C4⋊#95

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC23×C4⋊C4×C59C2
socle, prime radicalC25×C59C23
cosocleC24×C59C24
hypercenterC23×C4⋊C4D59
hypocenterC59C2×C4⋊#95
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90672);