Finite Group Databasebeta

C2×C8×D472 #28558047

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×D472

Splittings

FittingC2×C82×C59 ⋊ C2
SylowC59 ⋊ C2×C8×D8

Subgroups

subgroupG/H
centerC22×C8D236
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC2×C82×C59C2
socleC23×C59C4×D4
prime radicalC22×D472C4
cosocleC42×C59C24
hypercenterC2×C82D59
hypocenterC59C2×C8×D8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 138926);