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(C103⋊C3)⋊D7 #16864503

order4326
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C103⋊C3)⋊D7

Splittings

Fitting, socle, derived, HallC7×C103 ⋊ C2×C3
HallC7×C103⋊C3 ⋊ C2
HallD721 ⋊ C3
HallC103⋊C3 ⋊ D7
SylowC103 ⋊ C3×D7
SylowC7 ⋊ D103⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C103C2×C3
LCSG ▷ C7×C103
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 110
transitive degreeμt(G) = 721

Polycyclic presentation:

2,3,7,103|c^a=c^6,d^a=d^102,d^b=d^56

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊(D103⋊C3), C3×(C103⋊C3)⋊D7, C3⋊((C103⋊C3)⋊D7), …
maximal normal subgroup ofΓL(1,𝔽8)⋊(D103⋊C3), C3×(C103⋊C3)⋊D7, C5×(C103⋊C3)⋊D7, …
maximal quotient of(C103⋊C9)⋊D7, C3×(C103⋊C3)⋊D7, C3⋊((C103⋊C3)⋊D7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4326, 21);