Finite Group Databasebeta

C2×#21426456 #28746907

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21426456

Splittings

FittingC2×C4×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×#2275

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC2×C59C23×C42
FrattiniC23C24×D59
FittingC2×C4×C4⋊C4×C59C2
socleC24×C59C24
prime radicalC23×D236C22
cosocleC23×C59C25
hypercenterC2×C4×C4⋊C4D59
hypocenterC59C2×#2275
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

4694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 327786);