Finite Group Databasebeta

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C4×C23×C112⋊C3 #45688985

order33396
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C11

Aliases

direct productC4×C23×C112⋊C3
unambiguous semidirect product(C4×C112)⋊(C3×C23)
unambiguous semidirect product(C4×C112×C23)⋊C3

Splittings

Fitting, HallC4×C112×C23 ⋊ C3
derived, SylowC112 ⋊ C3×C4×C23
HallC112×C23 ⋊ C3×C4
HallC4×C112 ⋊ C3×C23

Subgroups

subgroupG/H
center, hypercenterC4×C23C112⋊C3
commutator, hypocenterC112C3×C4×C23
FrattiniC2C2×C23×C112⋊C3
FittingC4×C112×C23C3
socleC2×C112×C23C2×C3
prime radicalC2×C23×C112⋊C3C2
cosocleC2×C112C2×C3×C23
LCSG ▷ C112
UCSC1 ◁ C4×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Conjugacy classes & character table

3956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 49);