Finite Group Databasebeta

C4×#16837236 #28508866

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16837236

Splittings

SylowC59 ⋊ C4×M64

Subgroups

subgroupG/H
centerC4×C16C2×D59
commutatorC2×C59C2×C4×C16
FrattiniC2×C16C22×D59
FittingC2×C4×C16×C59C2
socleC22×C59C22×C16
prime radicalC23×C59C2×C16
cosocleC2×C16×C59C23
hypercenterC2×C4×C16D59
hypocenterC59C4×M64
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

250 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, 89745);