Finite Group Databasebeta

C2×#24908254 #35407973

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24908254

Splittings

SylowC83 ⋊ C2×#1953

Subgroups

subgroupG/H
centerC2×C4#14581767
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC22×#108×C83C2
socleC22×C83#389
prime radicalC24×C83C2×Q8
cosocleC22×C4×C83C24
hypercenterC22×#108D83
hypocenterC83C2×#1953
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 173137);