Finite Group Databasebeta

C22×Q8×D61 #16840585

order3904
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×D61

Splittings

FittingC22×Q8×C61 ⋊ C2
SylowC61 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC23C22×D61
commutator, cosocleC2×C61C25
FrattiniC2C24×D61
FittingC22×Q8×C61C2
socleC23×C61C23
prime radicalC23×D61C22
hypercenterC22×Q8D61
hypocenterC61C23×Q8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×Q8

850 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, 1372);