Finite Group Databasebeta

#410×D107 #28344915

order13696
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#410×D107

Splittings

Fitting#410×C107 ⋊ C2
SylowC107 ⋊ C2×#410

Subgroups

subgroupG/H
centerC4C22⋊C4×D107
commutatorC22×C107C23×C4
FrattiniC23C23×D107
Fitting#410×C107C2
socleC2×C107C22×C22⋊C4
prime radicalC2×#41×D107C2
cosocleC23×C107C24
hypercenter#410D107
hypocenterC107C2×#410
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1712

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12964);