Finite Group Databasebeta

#97×D409 #39909194

order26176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#97×D409

Splittings

Fitting#97×C409 ⋊ C2
SylowC409 ⋊ C2×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D409
commutatorC2×C409C2×C42
Fitting#97×C409C2
socleC22×C409C22×C4
prime radicalC22×D409C2×C4
cosocleC2×C4×C409C23
hypercenter#97D409
hypocenterC409C2×#97
LCSG ▷ C2×C409 ▷ C409
UCSC1 ◁ C2×C4 ◁ #97

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

4120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 496);