Finite Group Databasebeta

C4×#22547801 #44543191

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×#22547801

Splittings

SylowC499 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4C22⋊D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
FittingC4×Q8×C499C2
socle, prime radicalC22×C499C2×D4
cosocleC2×C4×C499C23
hypercenterC4×Q8D499
hypocenterC499C4×Q16
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

Conjugacy classes & character table

5008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 642);