Finite Group Databasebeta

#525×Dic61 #29838477

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

Aliases

direct product#525×Dic61

Splittings

SylowC61 ⋊ C4×#525

Subgroups

subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
Fitting, prime radicalC2×C61×#525C2
socle, cosocleC23×C61C25
hypercenterC2×#525D61
hypocenterC61C4×#525
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#525

3902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 328032);