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C52×(C103⋊C3)⋊C4 #44525436

order30900
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×(C103⋊C3)⋊C4
unambiguous semidirect product(C103⋊C3)⋊(C4×C52)
unambiguous semidirect productDic103⋊(C3×C52)
unambiguous semidirect product(C5×Dic103)⋊(C3×C5)

Splittings

derived, SylowC103 ⋊ C3×C4×C52
HallC52×Dic103 ⋊ C3
HallC52×C103⋊C3 ⋊ C4
HallC52×C103 ⋊ C3×C4
HallDic103 ⋊ C3×C52
HallC103⋊C3 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52D103⋊C3
commutator, hypocenterC103C3×C4×C52
FrattiniC2C52×D103⋊C3
Fitting, socleC2×C52×C103C2×C3
prime radicalC2×C52×C103⋊C3C2
cosocleC2×C103C2×C3×C52
LCSG ▷ C103
UCSC1 ◁ C2×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10300

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 42);