Finite Group Databasebeta

C2×#21422050 #28498387

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422050

Splittings

FittingC2×C59×C4⋊C16 ⋊ C2
SylowC59 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8C22⋊D59
commutatorC4×C59C22×C16
FrattiniC4×C8C22×D59
FittingC2×C59×C4⋊C16C2
socleC23×C59C22⋊C8
prime radicalC22×D236C8
cosocleC4×C8×C59C23
hypercenterC2×C4⋊C16D59
hypocenterC59C2×D4⋊C16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4⋊C16

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 79266);