Finite Group Databasebeta

← Prev (#16861989) Next (#16861991) →

C7⋊#10597010 #16861990

order4172
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC7⋊#10597010

Splittings

Fitting, socle, derived, HallC7×C149 ⋊ C4
SylowC149 ⋊ Dic7
SylowC7 ⋊ #10597010

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C149C4
prime radical, cosocleC7×D149C2
LCSG ▷ C7×C149
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 156
transitive degreeμt(G) = 1043

Polycyclic presentation:

2^2,7,149|a^2=b,c^a=c^6,d^a=d^105,d^b=d^148

Conjugacy classes & character table

269 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊#10597010, C3×C7⋊#10597010, C3⋊(C7⋊#10597010), …
maximal normal subgroup ofΓL(1,𝔽8)⋊#10597010, C3×C7⋊#10597010, C5×C7⋊#10597010, …
maximal quotient ofC3×C7⋊#10597010, C3⋊(C7⋊#10597010), C5×C7⋊#10597010, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4172, 7);