Finite Group Databasebeta

C8×(C2×D59)⋊C8 #28479155

order15104
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×(C2×D59)⋊C8

Splittings

FittingC2×C82×C59 ⋊ C2
SylowC59 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4×C8C2×D59
commutatorC2×C59C2×C82
FrattiniC2×C42C22×D59
FittingC2×C82×C59C2
socleC23×C59C2×C42
prime radicalC23×D59C42
cosocleC2×C42×C59C23
hypercenterC2×C82D59
hypocenterC59C8×C22⋊C8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60034);