Finite Group Databasebeta

C4×#16837223 #28504007

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16837223

Splittings

SylowC59 ⋊ C4×#364

Subgroups

subgroupG/H
centerC4×C8D236
commutatorC4×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC42×C8×C59C2
socleC22×C59C2×C4⋊C8
prime radicalC23×C59C2×M16
cosocleC22×C8×C59C23
hypercenterC42×C8D59
hypocenterC59C4×#364
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C42×C8

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 84886);