Finite Group Databasebeta

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D5×#14274263 #34062159

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

Aliases

direct productD5×#14274263
unambiguous semidirect productC5⋊(C2×#14274263)

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C2×C3
HallC5×#14274263 ⋊ C2
HallC72×D5×C13 ⋊ C3
HallC72×C13 ⋊ C3×D5
HallC72×D5 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallD5×C13 ⋊ #3861
HallC5×C13 ⋊ C2×#3861
SylowC72 ⋊ D5×C13⋊C3
SylowC13 ⋊ D5×#3861
SylowC5 ⋊ C2×#14274263

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup of#50303893, AGL(1,𝔽5)×#14274263, #50303905, …
maximal normal subgroup of#50303893, AGL(1,𝔽5)×#14274263, #50303905, …
maximal quotient ofDic5×#14274263, C2×D5×#14274263

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 152);