Finite Group Databasebeta

#421×D107 #28345000

order13696
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#421×D107

Splittings

Fitting#421×C107 ⋊ C2
SylowC107 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
Fitting#421×C107C2
socleC2×C107C22×C22⋊C4
prime radicalC2×#41×D107C2
cosocleC2×C4×C107C24
hypercenter#421D107
hypocenterC107C2×#421
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 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, 13049);