Finite Group Databasebeta

#376×D107 #28338786

order13696
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#376×D107

Splittings

Fitting#376×C107 ⋊ C2
SylowC107 ⋊ C2×#376

Subgroups

subgroupG/H
centerC22×C4C22×D107
commutatorC2×C107C22×C42
FrattiniC23C23×D107
Fitting#376×C107C2
socle, cosocleC23×C107C24
prime radicalC23×D107C23
hypercenter#376D107
hypocenterC107C2×#376
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ #376

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6835);