Finite Group Databasebeta

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C4×#19127463 #35309584

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

Aliases

direct productC4×#19127463

Splittings

SylowC83 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23×C4C22⋊D83
commutatorC4×C83C43
FrattiniC23×C4C22×D83
FittingC2×C4×C4⋊C4×C83C2
socle, prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C4×#340
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1182 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, 74748);