Finite Group Databasebeta

C2×C4×C4⋊Dic107 #28338796

order13696
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic107

Splittings

SylowC107 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D107
commutatorC2×C107C22×C42
FrattiniC23C23×D107
FittingC22×C42×C107C2
socle, prime radicalC24×C107C23
cosocleC23×C107C24
hypercenterC22×C42D107
hypocenterC107C2×C4×C4⋊C4
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6845);