Finite Group Databasebeta

C4×C22⋊D101 #15692216

order3232
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D101

Splittings

FittingC22×C4×C101 ⋊ C2
SylowC101 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D101
commutatorC2×C101C22×C4
FrattiniC22C22×D101
FittingC22×C4×C101C2
socle, cosocleC22×C101C23
prime radicalC2×C22⋊D101C2
hypercenterC22×C4D101
hypocenterC101C4×D4
LCSG ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 107);