Finite Group Databasebeta

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C4×#19127468 #35309607

order21248
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#19127468

Splittings

SylowC83 ⋊ C4×#342

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic83
commutatorC22×C83C43
FrattiniC25C22×D83
FittingC2×C4×C22⋊C4×C83C2
socleC23×C83C2×C22⋊C4
prime radical, cosocleC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C4×#342
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 74771);