Finite Group Databasebeta

#575×Dic61 #30544100

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#575×Dic61

Splittings

SylowC61 ⋊ C4×#575

Subgroups

subgroupG/H
centerC2×C4C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#575C2
socleC22×C61C23×D4
cosocleC2×C4×C61C25
hypercenterC2×#575D61
hypocenterC61C4×#575
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

2842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033655);