Finite Group Databasebeta

Q8×(C22⋊D59)⋊C4 #28748548

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×(C22⋊D59)⋊C4

Splittings

FittingQ8×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingQ8×C22⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC22×C22⋊D59C23
hypercenterQ8×C22⋊C4D59
hypocenterC59C4×D4×Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 329427);