Finite Group Databasebeta

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C2×#24907338 #35402341

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#24907338

Splittings

SylowC83 ⋊ C2×#1771

Subgroups

subgroupG/H
centerC23×C4C22×D83
commutatorC22×C83C22×C42
FrattiniC22×C4C23×D83
FittingC2×C4×C4⋊C4×C83C2
socle, prime radicalC24×C83C22×C4
cosocleC22×C4×C83C24
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#1771
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 167505);