Finite Group Databasebeta

C4×C22⋊D97 #15690771

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

Aliases

direct productC4×C22⋊D97

Splittings

FittingC22×C4×C97 ⋊ C2
SylowC97 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D97
commutatorC2×C97C22×C4
FrattiniC22C22×D97
FittingC22×C4×C97C2
socle, cosocleC22×C97C23
prime radicalC2×C22⋊D97C2
hypercenterC22×C4D97
hypocenterC97C4×D4
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1552

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, 107);