Finite Group Databasebeta

C2×#21434879 #29459243

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21434879

Splittings

FittingC22×C22⋊C8×C59 ⋊ C2
SylowC59 ⋊ C2×#3190

Subgroups

subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×C22⋊C8×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837913C2
hypercenterC22×C22⋊C8D59
hypocenterC59C2×#3190
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

2374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1040122);