Finite Group Databasebeta

C2×#14519846 #16840771

order3904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14519846
unambiguous semidirect productD61⋊#107

Splittings

FittingC2×C8×C61 ⋊ C4
SylowC61 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22C4⋊#6923
commutatorC4×C61C22×C4
FrattiniC4C22×#6923
FittingC2×C8×C61C4
socleC22×C61C4⋊C4
prime radicalC22×D61D4
cosocleC4×D61C23
hypercenterC2×C8#6923
hypocenterC61C2×#107
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1558);