Finite Group Databasebeta

C4×#19127433 #35295002

order21248
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#19127433

Splittings

SylowC83 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC2×C42D332
commutatorC4×C83C2×C4×C8
FrattiniC2×C42C22×D83
FittingC42×C8×C83C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenterC42×C8D83
hypocenterC83C4×Q8⋊C8
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

5360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 60166);