Finite Group Databasebeta

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C4×C7×C47⋊C23 #44475488

order30268
automorphism?
homologyAbelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C47⋊C23
unambiguous semidirect product(C4×C47)⋊(C7×C23)
unambiguous semidirect product(C4×C7×C47)⋊C23

Splittings

Fitting, HallC4×C7×C47 ⋊ C23
derived, SylowC47 ⋊ C4×C7×C23
HallC7×C47 ⋊ C4×C23
HallC4×C47 ⋊ C7×C23

Subgroups

subgroupG/H
center, hypercenterC4×C7C47⋊C23
commutator, hypocenterC47C4×C7×C23
FrattiniC2C2×C7×C47⋊C23
FittingC4×C7×C47C23
socleC2×C7×C47C2×C23
prime radicalC2×C7×C47⋊C23C2
cosocleC2×C47C2×C7×C23
LCSG ▷ C47
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1316

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30268, 2);