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C4×C52⋊(C103⋊C3) #44525449

order30900
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊(C103⋊C3)
unambiguous semidirect product(C4×C52)⋊(C103⋊C3)
unambiguous semidirect product(C4×C103)⋊(C52⋊C3)

Splittings

Fitting, HallC4×C52×C103 ⋊ C3
derived, HallC52×C103 ⋊ C3×C4
HallC4×C103 ⋊ C52⋊C3
SylowC103 ⋊ C4×C52⋊C3
HallC4×C52 ⋊ C103⋊C3
SylowC52 ⋊ C4×C103⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C52⋊(C103⋊C3)
commutator, hypocenterC52×C103C3×C4
FrattiniC2C2×C52⋊(C103⋊C3)
FittingC4×C52×C103C3
socle, cosocleC2×C52×C103C2×C3
prime radicalC2×C52⋊(C103⋊C3)C2
LCSG ▷ C52×C103
UCSC1 ◁ C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6180

Conjugacy classes & character table

3444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 55);