Finite Group Databasebeta

C42×C4⋊Dic59 #28509768

order15104
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC42×C4⋊Dic59

Splittings

SylowC59 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C42C2×D59
commutatorC2×C59C2×C43
FrattiniC24C23×D59
FittingC2×C43×C59C2
socle, prime radical, cosocleC24×C59C24
hypercenterC2×C43D59
hypocenterC59C42×C4⋊C4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C42 ◁ C2×C43

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 90647);