Finite Group Databasebeta

C2×C4⋊Dic97 #15690765

order3104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic97

Splittings

SylowC97 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D97
commutatorC2×C97C22×C4
FrattiniC22C22×D97
FittingC22×C4×C97C2
socle, prime radicalC23×C97C22
cosocleC22×C97C23
hypercenterC22×C4D97
hypocenterC97C2×C4⋊C4
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3104

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3104, 101);