Finite Group Databasebeta

C2×#24905303 #35293928

order21248
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24905303

Splittings

SylowC83 ⋊ C2×#1279

Subgroups

subgroupG/H
centerC23×C4D332
commutatorC4×C83C2×C4×C8
FrattiniC2×C42C22×D83
FittingC22×C4×C8×C83C2
socle, prime radicalC24×C83C22⋊C4
cosocleC2×C42×C83C23
hypercenterC22×C4×C8D83
hypocenterC83C2×#1279
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

974 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, 59092);