Finite Group Databasebeta

C2×#21422848 #28557668

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21422848

Splittings

SylowC59 ⋊ C2×#1565

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC2×C4×M16×C59C2
socleC23×C59C2×C4⋊C4
prime radicalC24×C59C4⋊C4
cosocleC42×C59C24
hypercenterC2×C4×M16D59
hypocenterC59C2×#1565
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 138547);