Finite Group Databasebeta

#97×#92418 #29569364

order15616
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#97×#92418

Splittings

SylowC61 ⋊ C8×#97

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D61
commutatorC2×C61C42×C8
FittingC4×#97×C61C2
socle, prime radicalC23×C61C2×C42
cosocleC2×C42×C61C23
hypercenterC4×#97D61
hypocenterC61C8×#97
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C4×#97

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 58919);