Finite Group Databasebeta

C2×#21422769 #28557013

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21422769

Splittings

SylowC59 ⋊ C2×#1546

Subgroups

subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC2×C59×#423C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC42×C59C24
hypercenterC2×#423D59
hypocenterC59C2×#1546
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

1246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 137892);