Finite Group Databasebeta

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#49150236

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC52×C13×C19 ⋊ C2×C3
HallC13×C19⋊(C52⋊C3) ⋊ C2
HallC52×D247 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ D13
HallD247 ⋊ C52⋊C3
HallC52×C19 ⋊ C3×D13
HallC52×C13 ⋊ D19⋊C3
HallC13×C19 ⋊ C2×C52⋊C3
SylowC52 ⋊ (C19⋊C3)⋊D13
SylowC19 ⋊ D13×C52⋊C3
SylowC13 ⋊ D19⋊(C52⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C19C2×C3
LCSG ▷ C52×C13×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Polycyclic presentation:

2,3,5^2,13,19|e^a=e^12,f^a=f^18,c^b=c^3d^4,d^b=c^3d,f^b=f^7

Conjugacy classes & character table

1063 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 62);