Finite Group Databasebeta

C4×#11758226 #16840232

order3904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11758226

Splittings

FittingC4×Q8×C61 ⋊ C2
SylowC61 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D61
commutatorC2×C61C23×C4
FrattiniC22C23×D61
FittingC4×Q8×C61C2
socle, cosocleC22×C61C24
prime radicalC2×#11758226C2
hypercenterC4×Q8D61
hypocenterC61C4×#41
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×Q8

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1019);