Finite Group Databasebeta

C2×D4×C107⋊C8 #28345134

order13696
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×C107⋊C8

Splittings

SylowC107 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D107
commutatorC2×C107C23×C8
FrattiniC2×C4C23×D107
FittingC2×C4×D4×C107C2
socleC23×C107C22×C4
prime radicalC22×D4×C107C4
cosocleC2×C4×C107C24
hypercenterC2×C4×D4D107
hypocenterC107C2×C8×D4
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 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, 13183);