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C2×C5×#14274263 #34062182

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#14274263

Splittings

Fitting, socle, HallC2×C5×C72×C13 ⋊ C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×C72×C13 ⋊ C2×C3
HallC2×C72×C13 ⋊ C3×C5
HallC2×C5×C72 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallC2×C5×C13 ⋊ #3861
HallC2×C72 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C2×#3861
SylowC72 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ C5×#3861
SylowC13 ⋊ C2×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC2×C5#14274263
commutator, cosocle, hypocenterC72×C13C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C72×C13C3
LCSG ▷ C72×C13
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×#21439522, C5×#21439524, C5×#21439532, …
maximal normal subgroup ofC5×#21439522, C5×#21439524, C5×#21439532, …
maximal quotient ofC4×C5×#14274263, C22×C5×#14274263

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 175);